The Physics of Space Flight

About this book

This introductory text covers all the key concepts, relationships, and ideas behind spaceflight and is the perfect companion for students pursuing courses on or related to astronautics. As a crew member of the STS-55 Space Shuttle mission and a full professor of astronautics at the Technical University of Munich, Ulrich Walter is an acknowledged expert in the field. This book is based on his extensive teaching and work with students, and the text is backed up by numerous examples drawn from his own experience. With its end-of-chapter examples and problems, this work is suitable for graduate level or even undergraduate courses in spaceflight, as well as for professionals working in the space industry. This third edition includes substantial revisions of several sections to extend their coverage. These include both theoretical extensions such as the study of relative motion in near-circular orbits, and more practical matters such as additional details about jet-engine and general rocket performance. New sections address regularized equations of orbital motion and their algebraic solutions and also state vector propagation; two new chapters are devoted to orbit geometry and orbit determination and to thermal radiation physics and modelling.

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Table of Contents

Frontmatter

Many people have had and still have misconceptions about the basic principle of rocket propulsion. Here is a comment of an unknown editorial writer of the renowned New York Times from January 13, 1920, about the pioneer of US astronautics, Robert Goddard, who at that time was carrying out the first experiments with liquid propulsion engines: “Professor Goddard … does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react – to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools.”

We now want to tackle the problem of solving the equation of rocket motion Eq. (1.​1.​7). As will be seen in Sect. 2.1, even for many simple cases it can be solved only by numerical methods. Since this is not the objective of this book, we will treat only those important cases that can be analyzed analytically. This will give rise to an important characteristic quantity the so-called “delta-v budget”. Its relevance will be explored in Sect. 2.4.1.

In Sect. 1.​3.​1, we found out that there are limits to the obtainable payload mass because of the finite structural mass. This limit is crucial for the construction of a rocket. If a rocket is to reach the low Earth orbit, a propulsion demand of about 9 km s−1 has to be taken into account (see end of Sect. 6.​4.​7), which is at the limit of feasibility for today’s chemical propulsions. If a higher payload ratio beyond 3% is required, or the S/C needs to leave the gravitational field of the Earth requiring a higher propulsion demand, one has to take measures to increase the rocket efficiency.

The thrust from thermal propulsion engines, such as jet engines, results from the exhaust of propellant gases, which is achieved by the rapid expansion of the heated gas. The heat usually comes from the combustion of chemical propellants—which we will assume in the following without loss of generality—or from the supply of external heat, or from both. A chemical propellant, therefore, serves two different purposes at the same time: it is a provider of mass for the required mass flow rate and a provider of energy to accelerate itself to ejection velocity.

Electric propulsion engines differ from thermal engines in that, among other things, the propellant does not serve as an energy source to heat and accelerate the propellant mass in the combustion chamber. Rather acceleration is achieved by accelerating ions in an electric field, the energy of which needs to be provided externally by an electric current source. This is both an advantage and a disadvantage at the same time. The advantage is that, theoretically, any amount of energy can be applied to the propellant mass which would in principle permit unlimited exhaust speeds, hence unlimited specific impulse, and therefore unlimited efficiency of the engine. The disadvantage is that the structural mass of the rocket stage increases due to the additional mass of the electric generator, which directly trades with payload mass. Massive generators are required especially for high-\( I_{sp} \) engines, so their additional mass may outweigh propellant savings. Therefore, comparisons between different propulsion systems always need to consider the total propulsion system mass: propulsion system, consumed propellant, plus energy supply system.

Now that we know the technical and physical properties of a rocket and the general equation of motion, which governs its flight, we are ready for a mission to the planets in our solar system. Before we investigate the rocket’s motion in interplanetary space, it first has to ascent in Earth’s gravitational field through the atmosphere. As will be shown later, ascent and reentry are subject to identical physical laws treated by the science called flight mechanics. The difference between the two is that reentry is powerless and the initial conditions of both mission phases are drastically different.

After ascent, we are now in outer space. How does a spacecraft move under the influence of the gravitational forces of the Sun, planets, and moons? This is the question we will deal with in this chapter, and we are pursuing general answers to it. Let us face reality from the start: The details of motions are usually very complicated and can be determined sufficiently accurately only numerically on a computer. This is exactly how real missions are planned. But the goal for us is not numerical accuracy, but to understand the basic behavior of a spacecraft. To achieve this, it suffices to study some crucial cases. The easiest and by far the most important case is the mutual motion of two point-like (a.k.a. ideal) bodies in the gravitational field of each other, the so-called (ideal) two-body problem (2BP), which we study in this chapter, such as the Moon in the gravitational field of the Earth. More complicated cases can often be traced back to the two-body problem by minor simplifications.

The most important maneuver in space is the one to change the orbit of a space vehicle. Because the initial and final orbits are subject to a central gravitational potential such a S/C will transit between two Keplerian orbits. This is true not only for planetary orbits but also for interplanetary flights with the Sun as the central body.

In fact, the first problem—to determine the orbit in the spheres of influence of different celestial bodies—is so serious that we cannot solve it exactly with analytical means. Hence, in practice, all interplanetary flights are determined only by complex numerical simulations. This enables one also to take even more complex situations into account, such as the so-called gravity-assist, weak stability boundary maneuvers, which we will discuss later, or even invariant manifolds (see Sect. 11.​5.​2). But as the important goal here is the basic understanding of orbit mechanics, we are seeking for a method to essentially describe the processes, albeit not precisely. This is indeed possible. The method is called “patched conics.”

After a spaceflight, the planetary entry (a.k.a. reentry for entry into Earth’s atmosphere) of a spacecraft is subject to the same aerodynamic and physical laws and equations (see Eqs. (6.3.6) and (6.3.7)) as ascent. One might therefore infer that the circumstances of both situations are the same.

In Chap. 7, we have looked at two point masses that were moving under their mutual gravitational influence. Formally speaking we were dealing with two bodies each with six degrees of freedom (three position vector components and three velocity vector components).

To delineate the general trajectory of a body mathematically or graphically one needs an observational space reference frame. In physics a reference frame is meant to be a concrete realization of a conceptional reference system with a choice of a coordinate system—meaning: a system of coordinates, such as rectangular (Cartesian), polar, or cylindrical coordinates, adapted to the symmetry of the problem—having a specific origin and orientation. (Note that “reference frame” and “coordinate system” are used in the literature almost synonymously.)

The general motion of a perfectly rigid body is the superposition of translation and rotation. We talked about translation under the influence of a gravitational field and possible external perturbations in the previous chapters. Now we want to have a look at the rotational behavior of a body.

The ultimate goal of this chapter is to determine the temperature equilibrium distribution inside a spacecraft (S/C) as a result of the thermal equilibrium with its space environment. Knowing these inside temperatures is essential when designing a S/C, as most components only work reliably within certain temperature ranges: batteries lose capacity and propellants may freeze.